This paper has been withdrawn by the author due to crucial issues detected in the revision of the manuscript, which forces to change completely the conclusions and rethink the objective of the investigation
We study a complex Dirac field in the chiral representation minimally coupled to gravity in 3+1 dimensions in the context of Einstein-Cartan theory. Generically the matter content gravitates in two different ways: On the one hand, the energy-momentum induces spacetime curvature; on the other hand, the presence of spin acts as a source for the spacetime torsion, which does not propagate. In this setup we consider the most general stationary spherically symmetric ansatz and we find an analytic black hole solution that supports a nontrivial spinor configuration. The spinor field affects the geometry by inducing spacetime torsion, though, remarkably, it does not alter the black hole metric, which retains its Schwarzschild form. We find solutions both in asymptotically flat and asymptotically (Anti) de Sitter spaces. Additionally, we consider how the solution gets deformed when the so-called Holst term is included in the gravity action. We discuss possible observational effects due to the coupling of fermions in the nonvanishing torsion background. Additionally we include a Maxwell field into the problem and find that it forces the spinor field to be zero. Finally, nonminimal couplings of the spinor with spacetime curvature are considered, obtaining any effect on the spherically symmetric solutions.
The behavior of a charged massive Dirac field on a Reissner-Nordstrom-AdS black hole background is investigated. The essential self-adjointness of the Dirac Hamiltonian is studied. Then, an analysis of the discharge problem is carried out in analogy with the standard Reissner-Nordstrom black hole case.
We evaluate quasinormal mode frequencies for RN black hole space times with cosmic string perturbed by a massless Dirac field, using Pöschl-Teller potential method. We find that only in the case of RN black hole having small charge, the effect due to cosmic string will dominate when perturbed by a negatively charged Dirac field, but if we are perturbing with positively charged Dirac field decay will be less in the case of black hole having cosmic string compared to the RN black hole without string
Using the tetrad formalism, we carry out the separation of variables for the massive complex Dirac equation in the gravitational and electromagnetic field of a four-parameter (mass, angular momentum, electric and magnetic charges) black hole.
Dirac equation for a general black hole metric having a cosmic string is derived. The quasi-normal mode frequencies for Schwarzschild, RN extremal, SdS and near extremal SdS black hole space-times with cosmic string perturbed by a massless Dirac field are obtained using WKB approximation and found that in all these cases, decay is less in black holes having cosmic string compared to black holes with out string.
In this paper we study the Dirac quasinormal modes of an uncharged 2 + 1 black hole proposed by Mandal et. al and referred to as MSW black hole in this work. The quasi- normal mode is studied using WKB approximation method. The study shows that the imaginary part of quasinormal frequencies increases indicating that the oscillations are damping and hence the black hole is stable against Dirac perturbations.
We calculated the Dirac Particles' Hawking radiation from the outer horizon of BTZ black hole via tunneling formalism. Applying WKB approximation to the Dirac equation in (2+1) dimensional BTZ spacetime background, we obtain the radiation spectrum for fermions and Hawking temperature of BTZ black hole. The results obtained by taking the fermion tunneling into account is consistent with the previous literatures.
We study charged fermionic perturbations in the background of two-dimensional charged Dilatonic black holes, and we present the exact Dirac quasinormal modes. Also, we study the stability of these black holes under charged fermionic perturbations.
We investigated Dirac Particles' Hawking radiation from event horizon of Kerr black hole in terms of the tunneling formalism. Applying WKB approximation to the general covariant Dirac equation in Kerr spacetime background, we obtain the tunneling probability for fermions and Hawking temperature of Kerr black hole. The result obtained by taking the fermion tunneling into account is consistent with the previous literatures.
Dirac cloud is in absence in general relativity since the superradiance mechanism fails to work for Dirac fields. For the first time we find a novel mechanism to support Dirac clouds, which is independent on superradiance mechanism. We study quasi bound states of Dirac particles around a charged spherical black hole in dilatonic gravity. We find that the quasi bound states become real bound states when the central black hole becomes extremal. We make an intensive study of the energy spectrum of the stationary clouds for different fine structure constant $μM$, and reveal the existence condition…
The behavior of a massive charged test Dirac field in the background of a Reissner-Nordström black hole is investigated. Especially, we obtain the frequencies of quasibound states by solving the Dirac equation numerically both in time and frequency domain. Our results suggest that although the absence of superradiance excludes the existence of stationary solutions for massive Dirac fields, it is still possible to find arbitrarily long-lived solutions.
With a generally covariant equation of Dirac fields outside a black hole, we develop a scattering theory for massive Dirac fields. The existence of modified wave operators at infinity is shown by implementing a time-dependent logarithmic phase shift from the free dynamics to offset a long-range mass term. The phase shift we obtain is a matrix operator due to the existence of both positive and negative energy wave components.
We study Hawking radiation of Dirac particles with spin-$1/2$ as a tunneling process from Schwarzschild-de Sitter and Reissner-Nordström-de Sitter black holes in background spacetimes with a spinning cosmic string and a global monopole. Solving Dirac's equation by employing the Hamilton-Jacobi method and WKB approximation we find the corresponding tunneling probabilities and the Hawking temperature. Furthermore, we show that the Hawking temperature of those black holes remains unchanged in presence of topological defects in both cases.
In a D-dimensional Lifshitz black hole we calculate exactly the quasinormal frequencies of a test Dirac field in the massless and zero angular eigenvalue limits. These results are an extension of the previous calculations in which the quasinormal frequencies of the Dirac field are determined, but in four dimensions. We discuss the four-dimensional limit of our expressions for the quasinormal frequencies and compare with the previous results. We also determine whether the Dirac field has unstable modes in the D-dimensional Lifshitz spacetime.
Motivated by the recent computations of the quasinormal frequencies of higher dimensional black holes we exactly calculate the quasinormal frequencies of the Dirac field propagating in D-dimensional (D > 4) massless topological black hole. From the exact values of the quasinormal frequencies for the fermion and boson fields we discuss whether the recently proposed bound on the relaxation time of a perturbed thermodynamical system is satisfied in D-dimensional massless topological black hole. Also we study the consequences of these results.
We study new type black holes in three-dimensional New Massive Gravity and we calculate analytically the quasinormal modes for fermionic perturbations for some special cases. Then, we show that for these cases the new type black holes are stable under fermionic field perturbations.
The Hawking radiation of Dirac particles in an arbitrarily rectilinearly accelerating Kinnersley black hole is studied by using a method of the generalized tortoise coordinate transformation. Both the location and the temperature of the event horizon depend on the time and polar angle. The Hawking thermal radiation spectrum of Dirac particles is also derived. PACS numbers: 97.60.Lf, 04.70.Dy
In a D-dimensional maximally symmetric spacetime we simplify the massless Dirac equation to two decoupled wavelike equations with effective potentials. Furthermore in D-dimensional Schwarzschild and Schwarzschild de Sitter black holes we note that for the massless Dirac field moving in the region exterior to the event horizon at least one of the effective potentials is not positive definite. Therefore the classical stability of these black holes against this field is not guaranteed. Here with the help of the S-deformation method, we state their classical stability against the massless Dirac fi…
Quantum thermal effect of Dirac particles in an arbitrarily accelerating Kinnersley black hole is investigated by using the method of generalized tortoise coordinate transformation. Both the location and the temperature of the event horizon depend on the advanced time and the angles. The Hawking thermal radiation spectrum of Dirac particles contains a new term which represents the interaction between particles with spin and black holes with acceleration. This spin-acceleration coupling effect is absent from the thermal radiation spectrum of scalar particles.
In this letter we derive new modes for massive Dirac field in the background of a higher-dimensional Schwarzschild black hole. We use in our approach the Cartesian gauge defined in local frames. We work in the context of ADD-like theories, assuming that the Standard Model fields (fermions and bosons) live only on a (3+1)-dimensional brane and the extra dimensions of space can be large in size.
The asymptotic form of Dirac spinors in the field of the Reissner-Nordstrom black hole are derived for the scattering states (with $E>mc^2$) obtaining the phase shifts of the partial wave analysis of Dirac fermions scattered from charged black holes. The elastic scattering and absorption are studied giving analytic formulas for the partial amplitudes and cross sections. A graphical study is performed for analysing the differential cross section (forward/backward scattering) and the polarization degree as functions of scattering angle.
Using the WKB approximation, massless and massive Dirac quasinormal modes (QNMs) are studied in spherically symmetric regular spacetimes. We analyze the relationships between QNM frequencies and the parameters (angular momentum number $l$, magnetic monopole charge $β$ and the mass of the field $m$), and discuss the extreme charge of magnetic monopole $β_{e}$ for spherically symmetric regular black holes (BHs). Furthermore, we apply an expansion method to expand QNMs in inverse powers of $L=l+1/2$, and confirm good precision with $l>n$. Finally, we improve traditional finite difference method t…
We study massive scalar fields and Dirac fields propagating in a five dimensional dilatonic black hole background. We expose that for both fields the physics can be describe by a two dimensional theory, near the horizon. Then, in this limit, by applying the covariant anomalies method we find the Hawking flux by restoring the gauge invariance and the general coordinate covariance, which coincides with the flux obtained from integrating the Planck distribution for fermions.
The Hawking radiation of Dirac particles in a charged Vaidya - de Sitter black hole is investigated by using the method of generalized tortoise coordinate transformation. It is shown that the Hawking radiation of Dirac particles does not exist for $P_1, Q_2$ components, but for $P_2, Q_1$ components it does. Both the location and the temperature of the event horizon change with time. The thermal radiation spectrum of Dirac particles is the same as that of Klein-Gordon particles.
It was investigated recently, with the aim of testing the weak cosmic censorship conjecture, whether an extremal Kerr black hole can be converted into a naked singularity by interaction with a massless classical Dirac test field, and it was found that this is possible. We generalize this result to electrically and magnetically charged rotating extremal black holes (i.e. extremal dyonic Kerr-Newman black holes) and massive Dirac test fields, allowing magnetically or electrically uncharged or nonrotating black holes and the massless Dirac field as special cases. We show that the possibility of t…
In this paper we study the quantum tunneling of Dirac magnetic monopoles from the global monopole black hole under quantum gravity effects. We start from the modified Maxwell's equations and the Generalized Uncertainty Relation (GUP), to recover the GUP corrected temperature for the global monopole black hole by solving the modified Dirac equation via Hamilton-Jacobi method. Furthermore, we also include the quantum corrections beyond the semiclassical approximation, in particular, first we find the logarithmic corrections of GUP corrected entropy and finally we calculate the GUP corrected spec…
We have studied quasinormal modes of spinor $\frac{1}{2}$, massless Dirac field perturbations of a black hole in massive gravity. The parameters of the theory, such as the mass of the black hole, the scalar charge of the black hole, mode number and the multipole number are varied to observe how the corresponding quasinormal frequencies change. We have also used the P$\ddot{o}$schl-Teller approximation to reach analytical values for the frequencies of quasinormal modes for comparison with the numerically obtained values. Comparisons are done with the frequencies of the Schwarzschild black hole.
The dirac quasinormal modes of the Reissner-Nordström black hole surrounded by quintessence are investigated using the third WKB approximation. We find that the magnitude of the imaginary part of the quasinormal mode frequencies increases firstly and then decreases as the charge $Q$ increases, but it decreases as the absolute value of $w_{q}$ increases. The magnitude of the imaginary part of quasinormal complex frequencies is smaller than those with no quintessence. That is to say, the dirac field damps more slowly due to the presence of quintessence.
The late-time evolution of Dirac field around spherically symmetric black hole surrounded by quintessece is studied numerically. Our results show, for lower values of the quintessence state parameter ε, Dirac field decays as power-law tail but with a slower decay rate than the corresponding Schwarzschild case. But for ε<-1/3, all the \ell-poles of the Dirac field give up the power-law decay form and relax to a constant residual field at asymptotically late times. The value of this residual field for which the field settles down varies on different surfaces. It has the lowest value on the black…
We study massive Dirac fields in the background of the near-horizon limit of the extremal Myers-Perry black hole in five dimensions. We consider the case in which both angular momenta have equal magnitude. The resulting Dirac equation can be decoupled into an angular and a radial part. The solution of the angular part results in some algebraic relations that determine completely the angular quantum numbers of the fermionic field. The radial part can be analytically solved in terms of special functions, which allow us to analyze the near-horizon radial current of the Dirac field.
In this paper, we study the existence of (quasi)bound states in two spacetime geometries describing Schwarzschild and Reissner-Nordström black holes. For obtaining this type of states we search for discrete quantum modes of the massive Dirac equation in the two geometries. After imposing the quantization condition, an analytical expression for the energy of the ground states is derived. The energy of higher states is then obtained numerically. For very small values of the black hole mass $M$ we compare the energy of the Reissner-Nordström black hole quasibound state with the Dirac-Coulomb ener…
We use the Dirac equation in a fixed black hole background and different independent techniques to demonstrate the absence of fermionic bound states around a Schwarzschild black hole. In particular, we show that no embedded eigenvalues exist which have been claimed for the case when the energy is less than the particle's mass. We explicitly prove that the claims regarding the embedded eigenvalues can be traced back to an oversimplified approximation in the calculation. We conclude that no bound states exist regardless the value of the mass.
The Hawking radiation of Dirac particles in an arbitrarily rectilinearly accelerating Kinnersley black hole with electro-magnetic charge and cosmological constant is investigated by using method of the generalized tortoise coordinate transformation. Both the location and the temperature of the event horizon depend on the time and the polar angle. The Hawking thermal radiation spectrum of Dirac particles is also derived. PACS numbers: 04.70.Dy, 97.60.Lf
Hawking effect of Dirac particles in a variable-mass Kerr space-time is investigated by using method of the generalized tortoise coordinate transformation. The location and the temperature of event horizon of the non-stationary Kerr black hole are derived. It is shown that the temperature and the shape of event horizon depend not only on the time but also on the polar angle. However, our results demonstrate that the Fermi-Dirac spectrum displays a new spin-rotation effect which is absent from that of Bose-Einstein distribution.
We update our previous work on the description of twisted configurations for complex massless scalar field on the Kerr black holes as the sections of complex line bundles over the Kerr black hole topology. From physical point of view the appearance of twisted configurations is linked with the natural presence of Dirac monopoles that arise as connections in the above line bundles. We consider their description in the gauge inequivalent to the one studied previously and discuss a row of new features appearing in this gauge.
In curved space-time, Hamilton-Jacobi equation is a semi-classical particle's motion equation, which plays an important role in the research of black hole physics. In this paper, starting from Dirac equation describing the spin 1/2 fermion and Rarita-Schwinger equation describing the spin 3/2 fermion respectively, we derive a Hamilton-Jacobi equation of the non-stationary spherically symmetric gravitational field background. Furthermore, the quantum tunneling behavior of a charged spherically symmetric black hole is investigated by using this Hamilton-Jacobi equation. The result shows that the…
The quasinormal modes of charged and uncharged massive scalar fields and also of charged Dirac fields against the background of a charged spherical black hole endowed with a scalar hair have been investigated. Special emphasis has been given to the case where negative scalar charge dominates over the electric charge of the black hole which mimics an Einstein-Rosen bridge. Except for the complete monotonic behaviour of the damping (imaginary part of the quasinormal mode) against the charge of the black hole as opposed to the existence of a peak for the pure RN case, the qualitative behaviour do…
Spontaneous loss of charge by charged black holes by means of pair-creation of charged Dirac particles is considered. We provide three examples of exact calculations for the spontaneous discharge process for 4D charged black holes by considering the process on three special non-rotating de Sitter black hole backgrounds, which allow to bring back the problem to a Kaluza-Klein reduction. Both the zeta-function approach and the transmission coefficient approach are taken into account. A comparison between the two methods is also provided, as well as a comparison with WKB results. In the case of n…
We investigate the Dirac and Klein-Gordon equations, as well as greybody radiation, for the Hayward black hole (BH) spacetime. We first consider the Dirac equation using a null tetrad in the Newman- Penrose (NP) formalism. The equations are then separated into angular and radial parts. A pair of one-dimensional Schrödinger like wave equations with effective potentials is obtained from the radial part. In order to examine the behavior of potentials, they are plotted with respect to radial distances. Additionally, the Klein-Gordon equation is considered in the Hayward BH spacetime. At the end, w…
Using the third-order WKB approximation and monodromy methods, we investigate the influence of Lorentz violating coefficient $b$ (associated with a special axial-vector $b_μ$ field) on Dirac quasinormal modes in the Schwarzschild black hole spacetime. At fundamental overtone, the real part decreases linearly as the parameter $b$ increases. But the variation of the imaginary part with $b$ becomes more complex. For the larger multiple moment $k$, the magnitude of imaginary part increases with the increase of $b$, which means that presence of Lorentz violation makes Dirac field damps more rapidly…
A stationary solution of the Dirac equation in the metric of a Reissner-Nordstrom black hole has been found. Only one stationary regular state outside the black hole event horizon and only one stationary regular state below the Cauchy horizon are shown to exist. The normalization integral of the wave functions diverges on both horizons if the black hole is non-extremal. This means that the solution found can be only the asymptotic limit of a nonstationary solution. In contrast, in the case of an extremal black hole, the normalization integral is finite and the stationary regular solution is ph…
We evaluate the quasinormal modes of massless Dirac perturbation in a Schwarzschild black hole surrounded by the free static spherically symmetric quintessence by using the third-order WKB approximation. The result shows that due to the presence of quintessence, the massless field damps more slowly. The real part of the quasinormal modes increases and the the absolute value of the imaginary part increases when the state parameter $w_q$ increases. In other words, the massless Dirac field decays more rapidly for the larger $w_q$. And the peak value of potential barrier gets higher as $|k|$ incre…
We consider the model of Dirac fermions coupled to gravity as proposed in \cite{VolovikBH}, in which superluminal velocities of particles are admitted. In this model an extra term is added to the conventional Hamiltonian that originates from Planck physics. Due to this term a closed Fermi surface is formed in equilibrium inside the black hole. In this paper we propose the covariant formulation of this model and analyse its classical limit. We consider the dynamics of gravitational collapse. It appears that the Einstein equations admit a solution identical to that of the ordinary general relati…
Quantum radiation properties of Dirac particles in general nonstationary black holes in the general case is investigated by both using the method of generalized tortoise coordinate transformation and considering the asymptotic behaviors of both the first and second order forms of Dirac equations near the event horizon. It is generally shown that the temperature and shape of event horizon of this kind of black holes depend on both the time and different angles. Further, we give a general expression of the new extra coupling effect in thermal radiation spectrum of Dirac particles which is missin…
We find the low lying quasinormal mode frequencies of the recently proposed novel four dimensional Gauss-Bonnet de Sitter black holes for scalar, electromagnetic and Dirac field perturbations using the third order WKB approximation as well as Padé approximation, as an improvement over WKB. We figure out the effect of the Gauss-Bonnet coupling $α$ and the cosmological constant $Λ$ on the real and imaginary parts of the QNM frequencies. We also study the greybody factors and eikonal limits in the above background for all three different types of perturbations.
So far the study of black hole perturbations has been mostly focussed upon the classical black holes with singularities at the origin and hidden by event horizon. Compared to that, the regular black holes are a completely new class of solutions arising out of modification of general theory of relativity by coupling gravity to an external form of matter. Therefore it is extremely important to study the behaviour of such regular black holes under different types of perturbations. Recently a new regular Bardeen black hole solution with a de Sitter branch has been proposed by Fernando. We compute …
We show asymptotic completeness for the massive charged Dirac equation between the black hole and Cauchy horizons of a sub-extremal ((Anti-) De Sitter) Reissner-Nordström black hole.
Hawking evaporation of Dirac particles and scalar fields in a Vaidya-type black hole is investigated by the method of generalized tortoise coordinate transformation. It is shown that Hawking radiation of Dirac particles does not exist for $P_1, Q_2$ components but for $P_2, Q_1$ components in any Vaidya-type black holes. Both the location and the temperature of the event horizon change with time. The thermal radiation spectrum of Dirac particles is the same as that of Klein-Gordon particles. We demonstrates that there is no new quantum ergosphere effect in the thermal radiation of Dirac partic…
Dirac equation is solved in the near horizon limit geometry of an extreme Kerr black hole. We decouple equations first as usual, into an axial and angular part. The axial equation turns out to be independent of the mass and is solved exactly. The angular equation reduces, in the massless case, to a confluent Heun equation. In general for nonzero mass, the angular equation is expressible at best, as a set of coupled first order differential equations apt for numerical investigation. The axial potentials corresponding to the associated Schrodinger-type equations and their conserved currents are …
We consider the behavior of massive Dirac fields on the background of a charged de-Sitter black hole. All black hole geometries are taken into account, including the Reissner-Nordström-de-Sitter one, the Nariai case and the ultracold case. Our focus is at first on the existence of bound quantum mechanical states for the Dirac Hamiltonian on the given backgrounds. In this respect, we show that in all cases no bound state is allowed, which amounts also to the non-existence of normalizable time-periodic solutions of the Dirac equation. This quantum result is in contrast to classical physics, and …
The evolution of electromagnetic and Dirac perturbations in the spacetime geometry of Kehagias-Sfetsos(KS) black hole in the deformed Horava-Lifshitz(HL) gravity is investigated and the associated quasinormal modes are evaluated using time domain integration and WKB methods. We find a considerable deviation in the nature of field evolution in HL theory from that in the Schwarzschild spacetime and QNMs region extends over a longer time in HL theory before the power-law tail decay begins. The dependence of the field evolution on the HL parameter $α$ are studied. In the time domain picture we fin…
We describe a thermal atmosphere around a black hole as vacuum excitations near to gravitational radius of a contracting thin black shell, i.e., in terms of properties of the physical vacuum of fields around a thin shell of mass $M$ collapsing from infinity to the Schwarzschild radius according to an external stationary observer. A natural explanation is introduced for the necessary cutoff using the equations of motion of the shells. We make a thermodynamic description of a fermionic field near the gravitational radius. Then a solution to the species problem for two fields, scalar one and spin…
We study the quasinormal modes of massive Dirac spinors in the background of rotating black holes. In particular, we consider the Kerr geometry as well as the five dimensional Myers-Perry spacetime with equal angular momenta. We decouple the equations using the standard methods from the literature. In the five dimensional Myers-Perry black hole the angular equation is solved analytically. Using the continued fraction method, we calculate the spectrum of quasinormal modes for the ground modes and first excited modes. We analyze, in a systematic way, its dependence on the different parameters of…
We construct a conformal scattering theory for Dirac fields in the interior of a Reissner-Nordström-like black hole, between the black hole event horizon and the Cauchy horizon. The main result is a resolution of the characteristic Cauchy problem for the Dirac equation on the horizons by solving a system of wave equations and re-interpreting its solution as the components of the required Dirac solution.
We study Chern-Simons black holes in d-dimensions and we calculate analytically the quasinormal modes of fermionic perturbations. Also, we consider as background the five-dimensional Chern-Simons black hole with torsion and the BTZ black hole with torsion. We have found that the quasinormal modes depend on the highest power of curvature present in the Chern-Simons theory, such as occurs for the quasinormal modes of scalar perturbations. We also show that the effect of the torsion is to modify the real part of the quasinormal frequencies, which modify the oscillation frequency of the field for …
We present the Fermi story of strong cosmic censorship in the near-extremal Reissner-Nordstrom-de Sitter black hole. To this end, we first derive from scratch the criterion for the quasi-normal modes of Dirac field to violate strong cosmic censorship in such a background, which turns out to be exactly the same as those for Bose fields, although the involved energy momentum tensor is qualitatively different from that for Bose fields. Then to extract the low-lying quasi-normal modes by Prony method, we apply Crank-Nicolson method to evolve our Dirac field in the double null coordinates. As a res…
